Solids mixing modeling

Figure 38. Experimental solids mixing data and model predictions—0.254 m jet, Set Point 3, Sampling Port A.

A hydrodynamic model of fluidization attempts to account for several essential features of fluidization mixing and distribution of solids and fluid in a so-called emulsion region, the formation and motion of bubbles through the bed (the bubble region ), the nature of the bubbles (including their size) and how they affect particle motion/distribution, and the exchange of material between the bubbles (with little solid content) and the predominantly solid emulsion. Models fall into one of three classes (Yates, 1983, pp. 74-78) ... 

It is important to emphasize here that, theoretically, if a solid mixture is ideal, intracrystalline distribution is completely random (cf section 3.8.1) and, in these conditions, the intracrystalline distribution constant is always 1 and coincides with the equilibrium constant. If the mixture is nonideal, we may observe some ordering on sites, but intracrystalline distribution may still be described without site interaction parameters. We have seen in section 5.5.4, for instance, that the distribution of Fe and Mg on Ml and M3 sites of riebeckite-glaucophane amphiboles may be approached by an ideal site mixing model—i.e.. 

The dispersion model of solids mixing (Kunii and Levenspiel, 1991) is based on Tick s equafion which describes unsfeady-sfafe mass transfer in one dimension. Thus... 

Vazquez and Calvelo (1983b) presented a model for the prediction of the minimum residence time in a fluidized bed freezer which can then be equated to the required freezing time. The model is defined in terms of a longitudinal dispersion coefficient D, which is a measure of the degree of solids mixing within the bed in the direction of flow (and has the dimensions of a diffusivity, and hence units of m s ), a dimensionless time T... 

Rottenbacher, L., Schofiler, M. and Bauer, W., Mathematical modelling of alcoholic fermentation in a gas/solid bioreactor - combined effects of solids mixing and non-steady-state kinetics. Proceedings of the First IFAC Symposium on Modelling and Control of Biotechnological Processes, Noordwijkerhout, 1985b, 151-157. 

Consider the reactor of Fig. 26.1(constant flow rates of both solids and gas into and out of the reactor. With the assumption of uniform gas concentration and mixed flow of solids, this model represents a fluidized-bed reactor in which there is no elutriation of fine particles. 

Emulsion phase in completely mixed state General solution—bubble phase free of solids (Orcutt model) In the following, the simplified Orcutt-Davidson-Pigford model (Orcutt et al., 1962) is presented. This model assumes in addition that the bubble phase is free of solids, and thus yh = 0. This means that the reaction takes place only in the emulsion (dense) phase. Then, the third term in eq. (3.516) disappears. The gas flow is in the inlet of the bed ,A, the particulate phase wfmA, and the bubble phase wswfmA, where A is the cross-sectional area of the bed and (eq. 3.476)... 

The liquid and solid phases are often supposed to be well-mixed, and a perfect mixing model can be applied to model the species-concentration profile. However, many expressions for the description of axial dispersion in the liquid phase in a BSCR are given in the literature [37,38]. 

Solid-Solution Models. Compared with the liquid phase, very few direct experimental determinations of the thermochemical properties of compound-semiconductor solid solutions have been reported. Rather, procedures for calculating phase diagrams have relied on two methods for estimating solid-solution model parameters. The first method uses semiem-pirical relationships to describe the enthalpy of mixing on the basis of the known physical properties of the binary compounds (202,203). This approach does not provide an estimate for the excess entropy of mixing and thus... 

Figure 3. Relationship between leaf area (A), epidermal cell density (B), stomatal density (C) and stomatal index (D) versus altitude for Nothofagus solandri leaves growing on the slope of Mt. Ruapehu, New Zealand (collected in 1999). Black diamonds indicate the mean of ten counting fields on each leaf, white squares are the averages of five to eight leaves per elevation, with error bars of 1 S.E.M. Nested mixed-model ANOVA with a general linear model indicates significant differences for all factors (p = 0.000). Averages per elevation were used for regression analysis A. y = -0.0212 + 73.1 R2 = 0.276 p = 0.147. B. y = 1.70 + 3122 R2 = 0.505 p = 0.048. C. y = 0.164 + 360 R2 = 0.709 p = 0.009. D. linear (dashed) y = 0.004 + 9.33 R2 = 0.540 p = 0.038 non-linear (solid) y = 0.00001 2 - 0.0206 + 21.132 R2 = 0.770.

What follows is a survey of the fluid-mechanical principles of fluidization technology, gas and solid mixing, gas-solid contact in the fluidized bed, typical industrial applications, and approaches to modeling fluidized-bed reactors. Further information is given in... 

For the calculation of solid-solution mineral behavior, two conceptual models may be used the end-member model (arbitrary mixing of two or more phases) and the site-mixing model (substituting elements can replace certain elements only at certain sites within the crystal structure). 

In the version 7.2 of the program EQ 3/6, the modeling of solid-solution minerals using end-member and site-mixing models (chapter 1.1.4.1.3) had been already realized compared to the PHREEQC version from 1995. Table 20 represents the solid-solution minerals that are considered in Gemboch s data set of EQ 3/6. Using the concept of solid-solution minerals, surface complexation can be modeled as well. 

Bader et al. (1988) used common salt as a solid tracer, which was injected into a flowing catalyst bed. Solids samples, withdrawn downstream of tracer injection, were leached with water and the salt concentration determined by electrical conductivity of the solution. Their results indicated substantial solids backmixing. Li et al. (1991) observed solids mixing in a fast fluidized bed combustor by using raw coal as a tracer, which was injected into the ash bed. Their results also showed that near-perfect mixing prevailed. Similar experiments was also conducted by Chesonis et al. (1991) in a cold model. 

For gas velocities ranging 4.1 to 6.3 m/s, the measured axial solids dispersion coefficients Ds varied from 0.39 to 0.91 m2/s for dilute solid suspension, while for the whole fast bed, in the same gas velocity range, Ds was 0.22 to 1.67 m2/s. Axial solid dispersion coefficient generally increases with both gas velocity and solids circulation rate. Milne and Berruti (1991) have also given their own model for solids mixing. 

Diffraction Methods in Inorgaitic Chemistry Electronic Structure of Solids Mixed Valence Compounds Oxides Solid-state Chemistry Solids Computer Modeling. 

The chemistry component of the model is, in most aspects, identical to the chemistry of the classical models of fluidized bed gasification. A major difference between the classical reactor models and the present fluidized bed coal gasifier computer model is that the classical models require specification of the bed hydrodynamics, such as bubble size. The present model can predict bubble size and the associated solids mixing. Again it is expected that the two types of models are complimentary. The present model can be used to define the hydrodynamics in the hot reactive environment and these hydrodynamics (e.g., bubble size) can then be used as... 

Fig. 17.6 Hourly observed solid) and modelled dashed) surface ozone mixing ratio in August 2006 at Hanyuu in Saitama prefecture (a) and Kodaira in Tokyo (b)...

These studies of particle mixing in marine sediments make it clear that particle transport in the upper 10 cm of the sediment column has important elfects on the distribution of reactive solids in the sediment column. While simple, diffusive mixing models explain many features of particle mixing, it is important to allow for more complex features of infaunal behavior selective transport of fine-grained, fresh sediment particles over coarser, older particles and transport over longer depth scales than can be explained by simple, diffusive mixing models. These transport... 

---